We will define our measure of variable importance (VI) in terms of a predictive skill measure \(V(f,P)\)  (the same measure in [1]}). Larger values of \(V(f,P)\)  should indicate better predictive performance. For \(Z = (X, Y)\) , we denote \(\dot{V}(f, P; \delta P)\)  as the Gateaux derivative of \(V(f,P)\)  at \(P\)  in the direction \(\delta P\) .
Specifically, one of the predictive skill measures we consider is the negative mean squared error (MSE):
\(V(f, P) = - \mathbb {E}_{(X, Y)\sim P} [Y - f(X)]^2,\) 
